A circular knitting needleat least 29’’ long of the right size to achieve the desired gauge. A longer needle is easier to use, but it cannot exceed double your cast-on row in length (not hard considering the longest I've ever seen is 40'').

You will be knitting the scarf on the long edge rather than the more conventional short edge. Therefore my use of length and width refers to the finished piece and does not conform to the standard parlance for straight knitting, where width is usually calculated in stitches and length in rows.

The Basic Concept

The idea is that you will be casting on enough stitches to achieve the length of the scarf. You will then pull the two ends of the cast-on together as if you were joining for regular circular knitting. However, instead of joining and knitting a tube, you will put a half twist in the cast-on row, and then pick up new stitches on the bottom edge of the cast-on. This will result in the needle being looped around, and twice as many stitches will be on the needle than were initially cast on. When you have finished picking up stitches, you should also be back at the first stitch you had initially cast on. You then simply knit around and around until the piece is the right width, and then cast off.

Structural Restrictions and Details

Ideally, the scarf must have a ratio of 3 or more to 1, length::width, so a 30’’ long scarf can be up to but not more than 10’’ wide. 30’’ is an excellent length for bulky weight yarn, as the resulting fabric is too thick to double comfortably anyway. A slightly longer scarf of a lighter weight yarn can be doubled to be a snug collar if it is very cold, and yet still works as a single layer. A longer scarf of about 40’’-45’’ that is 15’’ wide can be doubled and one loop pulled up to use as a cowl. I have made a stole that was 44'' in circumference and 22'' wide. This worked very well, but this sort of width would not be possible in a shorter piece. Also, the fabric needs to be very light and airy for this to work.

Since you establish the length of the piece from the cast-on row and are then stuck with it for the rest of the scarf, you must take a gauge. When you have determined the appropriate gauge and have selected the correct sized needle, do the math to determine the number of stitches you will be casting on for the length scarf you want. For example; if you are knitting 5st/in. and you want a 35’’ scarf, you need to cast on 175 stitches. Gauge in rows is less important if you are ‘winging it’ but extremely necessary if you plan on knitting elaborate patterns or regular repeats, as you are limited to the total number of rows you will be knitting. (I wing it a lot these days. I usually use a worsted weight yarn on US#8 needles and cast on 120 stitches. I work in either a 2x2 diagonal rib or a basket weave pattern until the piece is about 7 inches wide, work at least 2 rows of seed stitch, and then cast off.)

Each row of knitting takes you once around all 350 stitches and will actually add 2 rows to the width of the scarf. You will be knitting from the cast-on row outward. 5 rows of stockinette will equal 10 rows in the width of the scarf.

5 rows of stockinette will look like 5 rows of stockinette next to 5 rows of reverse stockinette. Therefore, for 6 alternating lengthwise stripes of stockinette and reverse stockinette each 5 rows wide, you need only knit 5 rows of stockinette, 5 rows of reverse stockinette, and then 5 rows of stockinette again.

Casting On, Casting Off

I have been converted to the invisible cast-on for my Möbius scarves. It is perfect for this as you pick up what would normally be left to graft later, and then remove the scrap yarn or string and weave in the little tail when you are done. If you are willing to use it, the invisible cast-on is much better. It uses less yarn, is more elastic and really is invisible compared to a cast-on with a bound edge. With the invisible cast-on, mark the first stitch you pick up off the bottom of your cast-on as the first stitch and start any patterning you may wish to do immediately. If you use a long tail cast-on, knit on, or any other cast-on which has a bound bottom edge, it is best to pick up the new stitches k1 p1 or else you will leave a ridge on one half of the finished piece. When using any of these other cast-ons, mark the first stitch of the initial cast-on as the first stitch.

Always mark the beginning of your row on the needle, or else you can and will lose track of whether you are at the beginning or in the middle of a row. Just do it, it prevents heartache and headaches later.

When casting off keep in mind that some stitches curl. When using stockinette stripes, I always finish with a stripe of K1P1 seed stitch for a neat edge. Also cast off loosely, as you would for a sweater neck. If you scale this up and work a stole however, bind off tightly, or crochet around the edge leaving out every third stitch. A stole requires a firmer, more defined edge to drape properly.

Step by step instructions for the faint of heart

For a 32’’x8’’ scarf, with a gauge of 4 stitches x 6 rows per square inch using a #6US circular needle that is 30’’ long.

With an invisible cast-on: Using the invisible cast-on, cast on 128 stitches. Carefully stretch the cast-on row so that you can see that the scrap string is taut. The needle which has the last worked stitch must be in your right hand. The slip knot of the invisible cast-on contrary to my original instructions does not have to be on the left hand needle.

Make sure that there are no twists in the cast-on row, and that the scrap string is parallel to the needle filament. Bring the two ends of the cast on together to form a loop, the yarn feed in your right hand and the slip knot in your left hand. This is exactly the same as if you were planning to knit a tube in the round, although the left needle tip will probably be dangling loosely. This is fine.

Holding the needles together, twist the slip-knotted end of the cast-on on the left either forward or back so that the string in that portion of the cast on is above the knitting needle/filament and so you can access the loops that are held by the string. This is a half twist. Be careful not to put a full twist or one and a half twists in the cast-on.

Place a stitch marker on the right hand needle tip, and begin knitting (KNIT every stitch) by pulling a stitch through each loop held by the string. You will only be using the right hand needle tip, just as you would if you were picking up stitches. You will eventually return to the stitch marker. This is the first row and will have 256 stitches total.

Slip the stitch marker onto the right needle tip again, and continue working in stockinette for 5 more rows. Then work 6 rows in reverse stockinette. Then work 6 rows in stockinette. Then work 6 rows in seed stitch. Cast off loosely. Go back and remove the scrap yarn by undoing the slip knot and pulling it out. Then, with a crochet hook, weave the tail left by the cast-off and the one from the cast-on into the piece.

With a bound edge cast-on: Cast on 128 stitches. Carefully stretch the cast-on row to within 2 inches of either end of the circular needle. The needle which has the last worked stitch must be in your right hand.

Make sure that there are no twists in the cast-on row, and that the bound edge is parallel to the needle filament. Bring the two cast-on ends together to form a loop, the yarn feed still in your right hand. This is exactly the same as if you were planning to knit a tube in the round, except that the left hand needle tip may be dangling. This is fine.

Holding the needles together, twist the end of the cast-on on the left hand needle forward or back so that the bound edge is above the knitting needle/filament. This is a half twist. Be careful not to put a full twist or one and a half twists in the cast-on.

Begin picking up stitches knitwise along the bound edge. As you are picking up stitches and not yet knitting, you will only be using the right hand needle tip. You will eventually reach the end of the bound edge, and return to the dangling needle. Make sure you have picked up 128 stitches. Place a stitch marker on the right hand needle after the last stitch you have picked up. This is the first row and will have 256 stitches total.

Continue by working in stockinette for 5 rows. Then work 6 rows in reverse stockinette. Then work 6 rows in stockinette. Then work 6 rows in seed stitch. Cast off loosely. Go back with a crochet hook and weave the tail left by the cast-off and the one from the cast-on into the piece.

Notes for those progressing beyond the basic

A note for those who would like to try repeating patterns that run in panels along the length: If you are doing a pattern with a right side and a wrong side, you will see both. In order to capitalize on this, I did a shawl with 22 repeats of 44 stitches; divided in half this is an odd number of repeats. This means that when I reached the half turn, right sides and wrong sides matched up. I don't know if this is clear so look at this little ascii:

Normally, if an even number of reps is knitted, it will look like this above the cast-on: RWRWRWRW, and like this below the cast-on:
WRWRWRWR

BUT, if you do an odd number, it will look like this above the cast-on:
RWRWRWR, and like this below the cast-on:
RWRWRWR

Additionally, any patterns you work will match up above and below like a clam shell with the cast-on seam as the hinge. The pattern will be upside-down, but not backwards.

An Alternate Technique

If you prefer straight knitting. You can also use the invisible cast-on to cast on the width of the scarf. Then, work straight for the desired length, put a 1/2 twist into the length and graft the two ends together. This is the technique I used to make a cable knit scarf with the reversible cable running the length (rather than the width) of the scarf.

* Note that 100g is for acrylic, or wool or other animal fiber yarns. Cotton, rayon, ramie, etc are much heavier than wool and will require more yarn. With yarns that are even part cotton, etc. be sure to purchase an extra ball (150g) in order to have enough.

How to fold a moebius loop - Lay out your scarf so that it looks like one of these (which one will depend on which way you twisted the cast-on row):

First, make fold 3 as square as possible. Then, grab the scarf at points A and B. Lift up to form a fold along the dotted line. Essentially you are lifting by the fold, and points x and y will drape down to meet. Keep lifting until folds 1 and 2 open out and the piece is flat. It will look like this (note where A and B are!):

The moebius loop is now neatly and compactly flat and can be folded or rolled up for storage.

Some terms

Stockinette or Stocking Stitch– A stitch which has two sides that differ greatly in appearance, the right side of which is all KNITs and the wrong side of which is all PURLs. When knit on straight needles, the right side is KNIT and the wrong side is PURLed. When knit in the round, every row is KNIT.

Reverse Stockinette – A stitch which has two sides that differ greatly in appearance, the right side of which is all PURLs and the wrong side of which is all KNITs. When knit on straight needles, the right side is PURLed and the wrong side is KNIT. When knit in the round, every row is PURLed.

Seed Stitch - A stitch which results in a completely reversible fabric, identical on both sides. Row 1: K1P1 to the end. Row 2 and all rows after: Knit the purls and purl the knits.

Picking up stitches – Picking up stitches is used for all sorts of shaping. Usually on an edge, one knits off of a loop of yarn occurring on the edge of the piece, rather than a live stitch. When knitting off of the invisible cast-on, one is actually knitting off live stitches.

Knit-wise or Purl-wise - Picking up a stitch or slipping a stitch as if one were going to KNIT or PURL into it.

Live stitches – loops of yarn which will unravel if left unsecured. A live stitch which is not knit or otherwise secured is referred to as dropped, and will unravel the entire column of stitches if it is not picked up.

How to take a gauge – One of the most tedious yet necessary things you will do. Cast on about 4 inches worth of stitches onto the needle which gives you the density of fabric which you want. Knit about 4 inches in rows. Then measure the piece flat and count how many stitches and how many rows equal a 3 inch square. Divide each figure by 3 and you have your gauge.

Invisible cast-on with scrap yarn - Slip knot the end of a length of cotton string or scrap yarn to the end of your yarn. Hold this slip knot against your right hand needle with your right hand. Hold the string and the yarn separate in your left hand. Holding the cotton string level, alternate pivoting the needle behind and in front of the string to pick up loops of yarn. This will create a figure 8 of alternating loops on the string and the knitting needle. The stitches on the cord are used as if they were LIVE but will not unravel if they are not knit. They are off-set from the stitches on the needle by 1/2 a stitch in width.

It is also possible to crochet a Möbius scarf. I'm going to assume that you know some basics of crocheting, at least by reading nocte's writeup. It can be helpful to make a Möbius bracelet or other small object first, just to get a handle on what's actually happening before diving into a more unwieldy project.

The basic process:

Chain stitch until you have a length that you like--hold both ends of the chain together and put it around your neck to test, and adjust as necessary.

Leave the hook in your last stitch, as though you were about to make another one. Let us pause for a moment to examine the chain you've just made. It has two ends: the end with the tail, where you started, and the end with the hook, where you last worked the yarn. It also has two sides. One of them looks like a row of V shapes or a braid. For simplicity's sake, I'm going to call this the front. The other side looks like a chain of links and bars. I'll similarly call this the back.

Lay the chain down on a flat surface, front side up, making sure there are no twists. The hook should still be in your last stitch.

Grasp both ends of the chain. Lift them up and bring them together. If you imagine that the loop they make is a very shorttube, the front surface will be on the inside.

Begin crocheting into the tail end of the chain. You may wonder exactly where to poke your hook into that first stitch. Since you're looking at the back of this particular stitch, it should look something like two curved bits of yarn with a straighter bump in the middle. You only want to bring your new stitches around the outermost loop on the edge you're working, so put your needle between the bump and the curved bit that's farther from you.

This first stitch should join the two ends. Because of the way crochet works, this attachment has incorporated a twist. If you look carefully, it should already be a kind of Möbius strip. Had you turned the yarn to stitch into the front side instead, you would have started a tube.

Keep crocheting with your favorite stitch, taking care to pull the yarn through only that outer loop for each link in the chain. As you go, you should keep an eye on which part of your work has the single twist, and nudge the twist away from the part you're about to stitch into. This should help you avoid twisting the chain back, working into the front rather than the back, and turning it back into a tube (a common mistake).

When you come back to the place where your ends were joined together, you will notice a sort of ledge where the chain begins to have stitches coming out of it. Do you avoid that piece and crochet onto the flat edge? Not unless you want to make a tube! Just keep going over that ledge.

Again, I'd recommend practicing on a foundation chain of 15 stitches or so--you can see the entire surface easily and check whether or not you've strayed into tube-land.

The foundation chain will be the "center" of the width of fabric, and each half-traversal of the edge will add a row on alternating sides of it. So, if you're planning on making a pattern of changing stitches or colors, be sure to take that into account. Also, if you're using stitches that have an obvious back and front, one half (starting from the chain and going out to the edge) will be "facing" entirely in one direction, and the other half will be facing the other direction.